Finite Group Databasebeta

← C₂⁵×C₃² #64397

Subgroups — C₂⁵×C₃² #64397

Order 288.

2244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₃	C₃	1	4	yes	maximal, direct product factor
3	C₂³×C₃²	C₂²	1	155	yes	direct product factor
4	C₂⁴×C₃	C₂×C₃	1	124	yes	direct product factor
5	C₂²×C₃²	C₂³	1	155	yes	direct product factor
6	C₂⁵	C₃²	1	1	yes	characteristic, direct product factor, Sylow
7	C₂³×C₃	C₂²×C₃	1	620	yes	direct product factor
8	C₂×C₃²	C₂⁴	1	31	yes	direct product factor
9	C₂⁴	C₂×C₃²	1	31	yes	direct product factor
10	C₂²×C₃	C₂³×C₃	1	620	yes	direct product factor
11	C₃²	C₂⁵	1	1	yes	characteristic, direct product factor, Sylow
12	C₂³	C₂²×C₃²	1	155	yes	direct product factor
13	C₂×C₃	C₂⁴×C₃	1	124	yes	direct product factor
14	C₂²	C₂³×C₃²	1	155	yes	direct product factor
15	C₃	C₂⁵×C₃	1	4	yes	direct product factor
16	C₂	C₂⁴×C₃²	1	31	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂⁴×C₃²	C₂	direct (N × H)
2. C₂⁵×C₃	C₃	direct (N × H)
3. C₂³×C₃²	C₂²	direct (N × H)
4. C₂⁴×C₃	C₂×C₃	direct (N × H)
5. C₂²×C₃²	C₂³	direct (N × H)
6. C₂⁵	C₃²	direct (N × H)
7. C₂³×C₃	C₂²×C₃	direct (N × H)
8. C₂×C₃²	C₂⁴	direct (N × H)
9. C₂⁴	C₂×C₃²	direct (N × H)
10. C₂²×C₃	C₂³×C₃	direct (N × H)
11. C₃²	C₂⁵	direct (N × H)
12. C₂³	C₂²×C₃²	direct (N × H)
13. C₂×C₃	C₂⁴×C₃	direct (N × H)
14. C₂²	C₂³×C₃²	direct (N × H)
15. C₃	C₂⁵×C₃	direct (N × H)
16. C₂	C₂⁴×C₃²	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×C₃²	2
C₂⁵×C₃	3